Specialising finite domain programs with polyhedra

A procedure is described for tightening domain constraints of finite domain logic programs by applying a static analysis based on convex polyhedra. Individual finite domain constraints are over-approximated by polyhedra to describe the solution space over ninteger variables as an n dimensional polyhedron. This polyhedron is then approximated, using projection, as an n dimensional bounding box that can be used to specialise and improve the domain constraints. The analysis can be implemented straightforwardly and an empirical evaluation of the specialisation technique is given

Incremental closure for systems of two variables per inequality

Subclasses of linear inequalities where each inequality has at most two vari- ables are popular in abstract interpretation and model checking, because they strike a balance between what can be described and what can be efficiently computed. This paper focuses on the TVPI class of inequalities, for which each coefficient of each two variable inequality is unrestricted. An implied TVPI in- equality can be generated from a pair of TVPI inequalities by eliminating a given common variable (echoing resolution on clauses). This operation, called result , can be applied to derive TVPI inequalities which are entailed (implied) by a given TVPI system. The key operation on TVPI is calculating closure: satisfiability can be observed from a closed system and a closed system also simplifies the calculation of other operations. A closed system can be derived by repeatedly applying the result operator. The process of adding a single TVPI inequality to an already closed input TVPI system and then finding the closure of this augmented system is called incremental closure. This too can be calcu- lated by the repeated application of the result operator. This paper studies the calculus defined by result , the structure of result derivations, and how deriva- tions can be combined and controlled. A series of lemmata on derivations are presented that, collectively, provide a pathway for synthesising an algorithm for incremental closure. The complexity of the incremental closure algorithm is analysed and found to be O (( n 2 + m 2 )lg( m )), where n is the number of variables and m the number of inequalities of the input TVPI system

Integer polyhedra for program analysis

Polyhedra are widely used in model checking and abstract interpretation. Polyhedral analysis is effective when the relationships between variables are linear, but suffers from imprecision when it is necessary to take into account the integrality of the represented space. Imprecision also arises when non-linear constraints occur. Moreover, in terms of tractability, even a space defined by linear constraints can become unmanageable owing to the excessive number of inequalities. Thus it is useful to identify those inequalities whose omission has least impact on the represented space. This paper shows how these issues can be addressed in a novel way by growing the integer hull of the space and approximating the number of integral points within a bounded polyhedron

Quadtrees as an Abstract Domain

Quadtrees have proved popular in computer graphics and spatial databases as a way of representing regions in two dimensional space. This hierarchical data-structure is flexible enough to support non-convex and even disconnected regions, therefore it is natural to ask whether this datastructure can form the basis of an abstract domain. This paper explores this question and suggests that quadtrees offer a new approach to weakly relational domains whilst their hierarchical structure naturally lends itself to representation with boolean functions

Nutritional and cultural aspects of plant species selection for a controlled ecological life support system

The feasibility of using higher plants in a controlled ecological life support system is discussed. Aspects of this system considered important in the use of higher plants include: limited energy, space, and mass, and problems relating to cultivation and management of plants, food processing, the psychological impact of vegetarian diets, and plant propagation. A total of 115 higher plant species are compared based on 21 selection criteria

Deeply penetrating banded zonal flows in the solar convection zone

Helioseismic observations have detected small temporal variations of the rotation rate below the solar surface corresponding to the so-called `torsional oscillations' known from Doppler measurements of the surface. These appear as bands of slower and faster than average rotation moving equatorward. Here we establish, using complementary helioseismic observations over four years from the GONG network and from the MDI instrument on board SOHO, that the banded flows are not merely a near-surface phenomenon: rather they extend downward at least 60 Mm (some 8% of the total solar radius) and thus are evident over a significant fraction of the nearly 200 Mm depth of the solar convection zone.Comment: 4 pages, 4 figures To be published in ApJ Letters (accepted 3/3/2000

Low-degree multi-spectral p-mode fitting

We combine unresolved-Sun velocity and intensity observations at multiple wavelengths from the Helioseismic and Magnetic Imager and Atmospheric Imaging Array onboard the Solar Dynamics Observatory to investigate the possibility of multi-spectral mode-frequency estimation at low spherical harmonic degree. We test a simple multi-spectral algorithm using a common line width and frequency for each mode and a separate amplitude, background and asymmetry parameter, and compare the results with those from fits to the individual spectra. The preliminary results suggest that this approach may provide a more stable fit than using the observables separately

Detection of the linear radical HC4N in IRC+10216

We report the detection of the linear radical HC4N in the C-rich envelope of IRC+10216. After HCCN, HC4N is the second member of the allenic chain family HC_(2n)N observed in space. The column density of HC4N is found to be 1.5 10**12 cm**(-2). The abundance ratio HC2N/HC4N is 9, a factor of two larger than the decrement observed for the cyanopolyynes HC$_(2n+1)N/HC_(2n+3)N. Linear HC_4N has a 3-Sigma electronic ground state and is one of the 3 low-energy isomeric forms of this molecule. We have searched for the bent and ringed HC4N isomers, but could only derive an upper limit to their column densities of about 3 10**(12) cm**(-2).Comment: Preprint of 10 page

Closure Algorithms for Domains with Two Variables Per Inequality

Weakly relational numeric domains express restricted classes of linear inequalities that strike a balance between what can be described and what can be efficiently computed. Such domains often restrict their attention of TVPI constraints which are systems of constraints where each constraint involves, at most, two variables. This technical report addresses the problem of deriving an incremental version of the closure operation. In this operation, a new constraint is added to a system that is already closed, and the computational problem is how to efficiently close the augmented system